Integrable hierarchies of topological type from dressing transformations

We consider the class of hierarchies of integrable PDEs satisfying topological recursion coming from Deligne-Mumford moduli spaces of stable algebraic curves. Many classical examples like Korteweg – de Vries, nonlinear Schroedinger, Toda lattice equations belong to this class but there are many new hierarchies depending on continuous parameters. We construct a big family of such hierarchies with the help of the well known dressing transformations and their quantization